Towards Integrated Perception and Motion Planning with Distributionally\n Robust Risk Constraints

Safely deploying robots in uncertain and dynamic environments requires a\nsystematic accounting of various risks, both within and across layers in an\nautonomy stack from perception to motion planning and control. Many widely used\nmotion planning algorithms do not adequately incorporate inherent perception\nand prediction uncertainties, often ignoring them altogether or making\nquestionable assumptions of Gaussianity. We propose a distributionally robust\nincremental sampling-based motion planning framework that explicitly and\ncoherently incorporates perception and prediction uncertainties. We design\noutput feedback policies and consider moment-based ambiguity sets of\ndistributions to enforce probabilistic collision avoidance constraints under\nthe worst-case distribution in the ambiguity set. Our solution approach, called\nOutput Feedback Distributionally Robust $RRT^{*}$(OFDR-$RRT^{*})$, produces\nasymptotically optimal risk-bounded trajectories for robots operating in\ndynamic, cluttered, and uncertain environments, explicitly incorporating\nmapping and localization error, stochastic process disturbances, unpredictable\nobstacle motion, and uncertain obstacle locations. Numerical experiments\nillustrate the effectiveness of the proposed algorithm.\n